The NYT gives an interesting example of how identity fits with memory in an interview of Nobel Prize-winning neuroscientist Dr. Kandel:

So what’s the biggest problem in psychoanalysis? It’s memory!

What does he mean? Take his own memory as an example. His Nazi neighbours in Austria forced him to change his identity as a young boy.

I was 8 ½. Immediately, we saw that our lives were in danger. We were completely abandoned by our non-Jewish friends and neighbors. No one spoke to me in school. One boy walked up to me and said, “My father said I’m not to speak to you anymore.” When we went to the park, we were roughed up. Then, on Nov. 9, 1938, Kristallnacht, we were booted out of our apartment, which was looted. We knew we had to get out.

Then, when awarded a Nobel prize, his childhood memories blocked him from accepting Austrian efforts to give his identity back (or to claim his prize as their own).

Their newspaper people said, “Oh, wonderful, another Austrian Nobel Prize!” I said: “You’ve got this wrong. This is an American, an American Jewish Nobel Prize.” The president of Austria wrote me a note: “What can we do to recognize you?” I said, “I do not need any more recognition, but it would it be nice to have a symposium at the University of Vienna on the response of Austria to National Socialism.” He said, “That’s fine.” I’m very close to Fritz Stern, the historian, and he helped me put the symposium together. Ultimately, a book came out of it. It had a modest impact.

Insertion of memories is apparently easier than removal. Yet at the end of it all he indicates he does not approve of removing bad memories.

To go into your head and pluck out a memory of an unfortunate love experience, that’s a bad idea. You know, in the end, we are who we are. We’re all part of what we’ve experienced. Would I have liked to have had the Viennese experience removed from me? No! And it was horrible. But it shapes you.